基于二次型价值函数的双电机转矩同步系统有限集模型预测控制

FCS-MPC for Dual-motor Torque Synchronization System Based on Quadratic Form Cost Function

在多电机系统有限集模型预测控制(finite control set model predictive control,FCS-MPC)中,随着电机数量的增加,加权求和型价值函数中权重系数的数量也随之增加,整定变得困难。对此,在对双电机转矩同步系统进行统一建模的基础上,通过构造二次型价值函数,将3个权重系数的整定问题转化为1个权重系数矩阵的求解问题。在二次型价值函数中应用由离线求解算法得到的权重系数矩阵能够保证系统的李雅普诺夫稳定性,从而可在连续控制周期内保证各误差收敛。在齿轮传动双电机转矩同步控制系统实验平台上对该算法进行实验验证,结果表明:将离线自整定后的权重系数矩阵用于二次型价值函数中,能使FCS-MPC控制下电机的跟踪误差和同步误差具有良好的收敛性。从理论和实验上证明了基于二次型价值函数的FCS-MPC算法能保证各电机较好的跟踪性能和转矩同步性能,同时该控制策略为拓展到多电机系统提供了可能。

In the multi-motor system finite control set model predictive control(FCS-MPC), the tuning of weight coefficients in the weighted sum cost function(WSCF) is becoming complex when the number of motors increases.Based on the unified model of a dual-motor torque synchronization system, this paper replaced the WSCF with a quadratic form cost function(QFCF), thereby, the tuning of the three weight coefficients was converted into the solving of a weight coefficient matrix. The Lyapunov stability of system can be guaranteed by applying the weight coefficient matrix obtained by the offline solution algorithm to the QFCF, so the errors can be guaranteed to converge in the continuous control periods. Experiments were performed on a gear drive two-motor torque synchronization control system. The results show that, in the dual-motor FCS-MPC, the applying of the QFCF, whose weight coefficient matrix is auto-tuned offline, can make the tracking errors and synchronization error converge. This paper proves theoretically and experimentally that the FCS-MPC algorithm based on QFCF can ensure tracking performance and torque synchronization performance of the motors, meanwhile, the control strategy provides the possibility to expand to multi-motor system.